Which statement best justifies that the function is continuous for all real numbers?

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which statement best justifies that the function

h(x)=\sin(3x^{2}+6)

is continuous for all real numbers? (a) Because

\sin(3x^{2}+6)

contains no denominators or square-roots, there are no points where it is undefined, so it is continuous. (b) Because

\sin x

is differentiable everywhere, its composition with any function is automatically continuous. (c) Because both

\sin x

and the polynomial

3x^{2}+6

are continuous everywhere, and the composition of two continuous functions is continuous. (d) Because the range of

\sin x

is bounded between

-1

and

1

, eliminating discontinuities.